"Discussion of the principles which underlie... development of mathematical expression has been confined almost exclusively within the inner circle of mathematicians interested in the philosophy of their science. But well-nigh up to the close of last century the explanations of this development—especially with regard to Imaginary Quantity—were almost purely mystical: they really explained nothing, threw no light on the motives and processes of thought which obscurely prompted it, and thus left it as much of an enigma as ever. In recent years, however, a real endeavour has been made to unravel this long-standing difficulty in the development of algebraic symbolism; it is even averred that we have now at last a completely adequate explanation of it. The claim is... that the doctrine has been purged of its mystical implications. But... the claim outruns the performance: the purgation is not thorough..."